1. A company manufactures concrete blocks for construction purposes. We know that the weights of the individual concrete blocks are normally distributed with a mean value of 11 kg, and a standard deviation of 0.3 kg.

1. The company can be 99% confident that the any randomly selected concrete block has a weight within the interval
2. The probability that a concrete block weighs less than 10.5 kg is

The commute time X each working day has the mean of 1 hour and standard deviation of 0.3 hours.

(1) What is the approximate distribution of the average daily commute time for a period of 36 days, by the Central limit theorem? Include the parameters.

(2) Find the probability that the average daily commute time for this period is larger than 1.06 hours.

Question 3

Suppose that X and Y have the following joint probability distribution:

Find the followings:

1. E(Y)=
2. Var(X)=
3. Cov(X,Y)=
4. Correlation(X,Y)=

Particles of charge -60 E-6 C, +40 E-6 C, and – 95 E-6 C are placed along the x-axis at 0.2 m, 0.4 m and 0.6 m, respectively. (a) Calculate the magnitude of the net electric field x = 0.3 m. (b) Calculate the magnitude of the net force on the +40 E-6 C charge

A radioactive mass emits particles according to a Poisson process at a mean rate of 2.5 per second. Let T be the waiting time, in seconds, between emissions.

1-What is the median waiting time?

2-Find P(0.3 < T < 1.5).

3-If 3 seconds have elapsed with no emission, what is the probability that there will be an emission within the next second

The mass-spring-damper system has a 2 kg block is displaced by an amplitude of 50 mm and
released. Ifthc phase angle ofrcsponse is 84.17o, how many cycles (m) will be executed beforc
the amplitude is reduced to I mm. What are the undamped natural frequency m« and spring
constant k ifthc period ofdamped oscillation rs is 0.3 scc.

1. What is a p-value and how is it used to make a decision about the null hypothesis?
2. How is the p-value related to the test statistic?
3. Explain whether or not rejecting the null hypothesis makes the alternative hypothesis true and why.
4. If I conduct a hypothesis testing with Type I error set at 0.05 and a resulting p-value of 0.3, what would my conclusion be?

A five-year bond with a yield of 7% (continuously compounded) pays a 5.5% coupon at the end of each year.

1. What is the bond’s price?
2. What is the bond’s duration?
3. Use the duration to calculate the effect on the bond’s price of a 0.3% decrease in its yield.
4. Recalculate the bond’s price on the basis of a 6.7% per annum yield and verify that the result is in agreement with your answer to (c).

You're crafting a portfolio of two stocks. You plan to buy $3,000 worth of the first stock and $1,000 worth of the second stock. The standard deviation of the first stock is 20% and the standard deviation of the second stock is 40%. They have a correlation coefficient of 0.3. How volatile will the portfolio be? Answer in percent rounded to two decimal places. (e.g., 4.53% = 4.53)

A stock portfolio has an expected return of 12% and a standard deviation of 20%. A bond portfolio has an expected return of 6% and a standard deviation of 9%. The two portfolios have a correlation coefficient of 0.3. T-Bills have an expected return of 2%. Your coefficient of risk aversion is 7.

1. What is the expected return and standard deviation of the minimum variance portfolio?